Research Focus
Numerical analysis, scientific computing, and deep learning
I am interested in the study and development of numerical algorithms in applied mathematics. I mainly work in the following three areas: (1) Novel spectral methods for the solution of differential equations, (2) Low-rank techniques, and (3) Theoretical aspects of deep learning.
Publications
Dense networks that do not synchronize and sparse ones that do (with M. Stillman and S. H. Strogatz), Chaos, 30 (2020), 083142.
Fast algorithms using orthogonal polynomials (with S. Olver and R. M. Slevinsky), Acta Numerica, 29 (2020), pp. 573-699.
Stable extrapolation of analytic functions (with L. Demanet), Foundations of Computational Mathematics, 19 (2019), pp. 297-331.
Bounds on the singular values of matrices with displacement structure (with B. Beckermann), SIAM Review, 61 (2019), pp. 319-344.
Why are big data matrices approximately low rank? (with M. Udell), SIAM Journal on Mathematics of Data Science, 1 (2019), pp. 144-160.
In the news
- New center merges math, AI to push frontiers of science
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- Weiss teaching award honors eight exceptional faculty
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- Computing with rational functions
- Eleven assistant professors win NSF early-career awards
- 30 Arts & Sciences faculty honored with endowed professorships
- Grants create engagement opportunities for students
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